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Simplifying 10x4 + -14x2 + 3 = 0 Reorder the terms: 3 + -14x2 + 10x4 = 0 Solving 3 + -14x2 + 10x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.3 + -1.4x2 + x4 = 0 Move the constant term to the right: Add '-0.3' to each side of the equation. 0.3 + -1.4x2 + -0.3 + x4 = 0 + -0.3 Reorder the terms: 0.3 + -0.3 + -1.4x2 + x4 = 0 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + -1.4x2 + x4 = 0 + -0.3 -1.4x2 + x4 = 0 + -0.3 Combine like terms: 0 + -0.3 = -0.3 -1.4x2 + x4 = -0.3 The x term is -1.4x2. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x2 + 0.49 + x4 = -0.3 + 0.49 Reorder the terms: 0.49 + -1.4x2 + x4 = -0.3 + 0.49 Combine like terms: -0.3 + 0.49 = 0.19 0.49 + -1.4x2 + x4 = 0.19 Factor a perfect square on the left side: (x2 + -0.7)(x2 + -0.7) = 0.19 Calculate the square root of the right side: 0.435889894 Break this problem into two subproblems by setting (x2 + -0.7) equal to 0.435889894 and -0.435889894.Subproblem 1
x2 + -0.7 = 0.435889894 Simplifying x2 + -0.7 = 0.435889894 Reorder the terms: -0.7 + x2 = 0.435889894 Solving -0.7 + x2 = 0.435889894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x2 = 0.435889894 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x2 = 0.435889894 + 0.7 x2 = 0.435889894 + 0.7 Combine like terms: 0.435889894 + 0.7 = 1.135889894 x2 = 1.135889894 Simplifying x2 = 1.135889894 Take the square root of each side: x = {-1.065781354, 1.065781354}Subproblem 2
x2 + -0.7 = -0.435889894 Simplifying x2 + -0.7 = -0.435889894 Reorder the terms: -0.7 + x2 = -0.435889894 Solving -0.7 + x2 = -0.435889894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x2 = -0.435889894 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x2 = -0.435889894 + 0.7 x2 = -0.435889894 + 0.7 Combine like terms: -0.435889894 + 0.7 = 0.264110106 x2 = 0.264110106 Simplifying x2 = 0.264110106 Take the square root of each side: x = {-0.513916439, 0.513916439}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.065781354, 1.065781354, -0.513916439, 0.513916439}
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